Answer:
10.5 feet
Step-by-step explanation:
In this problem, we have two similar triangles:
- One consists of the mailbox, its shadow and the hypothenuse
- The other one consists of the tree, its shadow and the hypothenuse
The two triangles are similar, so they have same proportions between their sides: therefore, we can apply the rule of three:
[tex]\frac{m}{s_m}=\frac{t}{s_t}[/tex]
where
m = 36 in is the height of the mailbox
[tex]s_m=28 in[/tex] is the shadow of the mailbox
t is the height of the tree
[tex]s_t=98 in[/tex] is the length of the shadow of the tree
Solving for t, we find the height of the tree:
[tex]t=\frac{m\cdot s_t}{s_m}=\frac{(36)(98)}{28}=126 in[/tex]
And since
1 feet = 12 inches
The height of the tree in feet is
[tex]t=\frac{126}{12}=10.5 ft[/tex]
